The electron emission of a carbon nanotube-field emission display mainly depends on the electric field intensity of carbon nanotubes tip. So the accurate calculation of the electric field intensity of carbon nanotubes tip is very important for the development of carbon nanotube-field emission display. In calculating the electric field intensity in a carbon nanotube-field emission display, the field emission model of carbon nanotubes cathode have been simplified as 2D model in many reports for increasing the computation efficiency. To compare and analyze the differences between the calculated results obtained by using 2D and 3D models, single carbon nanotube 2D model, single carbon nanotube and single carbon nano-wall 3D models are constructed respectively, and the finite element simulation software Ansoft Maxwell is used. The calculated results indicate that 2D model field emission of carbon nanotubes cathode expresses the actual field emission of carbon nano-wall cathode, not the actual field emission of carbon nanotubes cathode. The electric field intensity of single carbon nanotube tip calculated by 2D model is only about 1/4 of actual electric field intensity of 3D carbon nanotube tip.